Visualizing Solutions of the One-Dimensional Schrödinger Equation Using a Finite Difference Method

Document Type

Article

Department or Administrative Unit

Chemistry

Publication Date

7-29-2022

Abstract

FINDIF is a Windows application that numerically solves the one-dimensional (1D) Schrödinger equation and displays the eigenstates, eigenvalues, and probability density of the system. FINDIF accepts both nonperiodic and periodic 1D potential energy functions as input and uses the finite difference method to evaluate the energy of the quantum system. This Technology Report illustrates the use of FINDIF with applications, such as the classic 1D particle-in-a-box, the particle-in-a-box with internal barrier, the modified Kronig–Penney model of a linear array of rectangular wells, the harmonic oscillator with visualization of the eigenstates and tunneling effect, the anharmonic Morse potential of the Ar dimer, and the periodic torsional potential for internal rotation of ethane. Students can explore other quantum chemical examples by considering both realistic and fictitious model potential energy functions, making outcome predictions before running FINDIF calculations, visualizing the results afterward, and then comparing their predictions with the results they observe. Such exercises assist students as they develop insights into the behavior and properties of quantum mechanical systems.

Comments

This article was originally published in Journal of Chemical Education. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Journal

Journal of Chemical Education

Rights

Copyright © Published 2022 by American Chemical Society and Division of Chemical Education, Inc.

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